Spreadsheet Accumulator Sizing for Hybrid Hydraulic Applications ...

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TARDEC ---TECHNICAL REPORT--- No._____________ By:______________________________________ Distribution:____________________________________ U.S. Army Tank-automotive and Armaments Research Development and Engineering Center Detroit Arsenal 6501 East 11 Mile Road Warren, Michigan 48397-5000 13942 Wesley Bylsma Approved for public release; distribution is unlimited. SPREADSHEET ACCUMULATOR SIZING FOR HYBRID HYDRAULIC APPLICATIONS USING THE BENEDICT-WEBB- RUBIN EQUATION OF STATE

Transcript of Spreadsheet Accumulator Sizing for Hybrid Hydraulic Applications ...

  • TARDEC

    ---TECHNICAL REPORT---

    No._____________ By:______________________________________

    Distribution:____________________________________

    U.S. Army Tank-automotive and Armaments Research Development and Engineering Center Detroit Arsenal 6501 East 11 Mile Road Warren, Michigan 48397-5000

    13942

    Wesley Bylsma

    Approved for public release; distribution is unlimited.

    SPREADSHEET ACCUMULATOR SIZING FOR HYBRID HYDRAULIC APPLICATIONS USING THE BENEDICT-WEBB-

    RUBIN EQUATION OF STATE

  • REPORT DOCUMENTATION PAGE Form Approved

    OMB No. 074-0188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503 1. AGENCY USE ONLY (Leave blank) 2. REPORT DATESEPTEMBER 2003

    3. REPORT TYPE AND DATES COVERED AUGUST SEPTEMBER 2003

    4. TITLE AND SUBTITLE SPREADSHEET ACCUMULATOR SIZING FOR HYBRID HYDRAULIC APPLICATIONS USING THE BENEDICT-WEBB-RUBIN EQUATION OF STATE

    5. FUNDING NUMBERS

    6. AUTHOR(S) Wesley Bylsma

    7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

    8. PERFORMING ORGANIZATION REPORT NUMBER

    U.S. Army Tank-automotive and Armaments Command/National Automotive Center ATTN: AMSTA-TR-N/MS157 Warren, MI 48397-5000

    13942

    9. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING / MONITORING AGENCY REPORT NUMBER

    11. SUPPLEMENTARY NOTES

    12a. DISTRIBUTION / AVAILABILITY STATEMENT Approved for public release: Distribution is unlimited

    12b. DISTRIBUTION CODE A

    13. ABSTRACT (Maximum 200 Words) A simple and effective method using optimization with the Benedict-Webb-Rubin equation of state is presented to size accumulator volumes in hybrid hydraulic applications given the pre-charge, minimum and maximum operating pressures.

    14. SUBJECT TERMS accumulator sizing, Benedict-Webb-Rubin, hybrid hydraulic

    15. NUMBER OF PAGES 6

    16. PRICE CODE

    17. SECURITY CLASSIFICATION OF REPORT

    Unclassified

    18. SECURITY CLASSIFICATION OF THIS PAGE

    Unclassified

    19. SECURITY CLASSIFICATION OF ABSTRACT

    Unclassified

    20. LIMITATION OF ABSTRACT

    Unclassified NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

    Prescribed by ANSI Std. Z39-18 298-102

  • ABSTRACT ...................................................................................................1

    1.0 INTRODUCTION....................................................................................1

    2.0 PRINCIPALS OF OPERATION .............................................................1

    3.0 ACCUMULATOR SIZING .....................................................................2

    4.0 CALCULATION......................................................................................2

    5.0 SPREADSHEET EXAMPLE...................................................................3

    6.0 SUMMARY/CONCLUSION ...................................................................5

    CONTACT .....................................................................................................5

    REFERENCES...............................................................................................5

    DEFINITIONS, ACRONYMS, ABBREVIATIONS .....................................5

    APPENDIX A BOSCH REXROTH APPLICATION NOTE.....................6

    FIGURE 1 TYPES OF ACCUMULATORS (SOURCE: PARKER HANNIFIN, HYDRAULIC ACCUMULATOR DIVISION) 1

    FIGURE 2 BWR CONSTANTS (NITROGEN)..................................... 2 FIGURE 3 MICROSOFT EXCEL SOLVER DIALOG SCREEN........... 3 FIGURE 4 SPREADSHEET EXAMPLE A.......................................... 4 FIGURE 5 SPREADSHEET EXAMPLE B .......................................... 4 FIGURE 6 SPREADSHEET EXAMPLE C.......................................... 5 FIGURE 7 SPREADSHEET EXAMPLE D.......................................... 5

  • 1

    Technical Report 13942 September 2003

    SPREADSHEET ACCUMULATOR SIZING FOR HYBRID

    HYDRAULIC APPLICATIONS USING THE BENEDICT-WEBB-RUBIN EQUATION OF STATE

    Wesley Bylsma

    U.S. Army Tank-automotive and Armaments Command Research, Development and Engineering Center

    National Automotive Center Warren, Michigan 48397-5000

    ABSTRACT A simple and effective method using optimization with the Benedict-Webb-Rubin equation of state is presented to size accumulator volumes in hybrid hydraulic applications given the pre-charge, minimum and maximum operating pressures. 1.0 INTRODUCTION In the automotive industry recent efforts have focused on ways to drive down operating costs by reducing fuel consumption requirements. The development of hybrid vehicleselectric and hybrid, and more recently fuel cells are examples of this interest. The main component of this approach is an energy storage device such as a capacitor for electric or an accumulator for hydraulic applications. The main operating principal is the assumption that the duty cycle of the system will consist of periods when 1) the system power demand is low, at which time excess energy can be stored, and 2) the system power demand is high, at which time the stored energy can be used to supplement the power demand. Reference to these periods is more commonly referred to as regenerative braking or power assist. An outline of the remainder of this report is as follows: Section 2 presents the principals behind the operation of an accumulator. Section 3 covers the factors affecting the size. Section 4 discusses the calculations to define the size. Section 5 gives an example of a spreadsheet solution. Section 6 gives a summary and conclusion 2.0 PRINCIPALS OF OPERATION The focus of this report is on energy storage sizing for the hybrid hydraulic solution. For this application accumulators are used as energy storage devices. These accumulators are based on the principle that gas is compressible and oil is incompressible. Oil flow into the accumulator compresses the gas by reducing its

    storage volume. Energy is stored by the volume of hydraulic fluid that compressed the gas under pressure. If the fluid is released will quickly flow out under the pressure of the expanding gas. This will also require a reservoir to store the fluid that has exited the accumulator or before it is pumped in. Some common types of accumulators are depicted in Figure 1. The main difference between them is in how the gas is confined to a specific volume. The rate at which compression and expansion of the gas takes place affects the gas state---which is defined by pressure, volume, and temperature. Slow rates are known as isothermal processes---the rate is so slow that the temperature of the gas is essentially constant. Fast rates are known as adiabatic processes---the rate is so fast that the temperature of the gas changes but not the surroundings (no gain or loss of heat). The relationship between pressure and volume is affected by these processes. Appendix A contains more specifics on these processes with correction factors for ideal gases. It is evident, however, that the temperature must be accounted for.

    Figure 1 Types of accumulators (Source: Parker Hannifin, Hydraulic Accumulator Division)

  • 2

    3.0 ACCUMULATOR SIZING Sizing is based on the gas charge of the accumulator. The change in volume and pressure determines how much fluid can be stored and released. To start the sizing process we begin with some defined quantities:

    0p - pre-charge at room temperature with-no fluid

    1p - minimum operating pressure

    2p - maximum operating pressure 0V - pre-charge volume

    1V - minimum pressure volume

    2V - maximum pressure volume V = 1 2V V - charge volume

    The pre-charge state plays a key role in sizing the accumulator. Common Rules of Thumb are:

    0 10.9p p

    to reduce bladder wear on the inlet valve,

    2 04p p for consideration of bladder elasticity performance (see Appendix A). From these conditions the pre-charge volume can be approximated from

    0 1.5...3V V .

    The reservoir is roughly three times the accumulator pre-charge volume to provide a low-pressure chamber. 4.0 CALCULATION We diverge here from the procedure outlined in Appendix A for a more accurate approach for temperature considerations. Departing from the ideal gas relationship

    PV mRT= we use the Benedict-Webb-Rubin (BWR) Equation of State ( p v T ) defined as

    ( )20

    0 0 2 2

    2 3 6 3 2

    1 vCB RT A c ebRT aRT aT vpv v v v v T

    + = + + + +

    Here eight experimental constants are used, with good prediction results up to about 2.5 cr , where cr is the density of the substance at the critical point. See [4].

    The gas is assumed to be nitrogen, which has well documented properties and whose coefficients for the BWR equation are shown in Figure 2. From the initial (pre-charge) pressure and accumulator volume the mass of the gas can be determined. Using the mass of the gas the minimum and maximum accumulator volume can be determined from the minimum and maximum pressures required and operating temperature at these points. The non-linearity of the BWR makes these determinations difficult and requires an iterative method.

    ( )

    ( )

    32

    22

    0

    3

    30.025102

    21.0536420

    20.0023277

    0.04074260

    728.41

    8059.00

    0.0001272

    0.005300

    la atmg mol

    lA atmg mol

    lbg mol

    lBg mol

    lc K atmg mol

    lC K atmg mol

    lg mol

    lg mol

    =

    =

    =

    =

    =

    =

    =

    =

    2

    0.0820544 l atmRg mol K

    =

    Figure 2 BWR constants (Nitrogen)

    An easy solution, however, is to use an optimization method. This technique requires a cost function to minimize. The cost function can be defined as

    ( )2desired BWRe p p= where BWRp (the BWR equation) is a function of variables m , V and T . The following procedure outlines the steps to determine the mass of the gas, and the minimum and maximum volumes required. 1) to find the initial mass of the gas set 0desiredp p= and

    ( )BWR BWRp p m= then optimize the cost function e

  • 3

    over the mass m . Note that this is really an optimization over the molar specific volume since

    0V lv Mm k mol

    =

    where the molar mass (for nitrogen) is

    28.013 kgMk mol

    =

    and the gas constant (for nitrogen) is

    0.2967uR kJRM kg K

    = =

    with a universal gas constant of

    8.314ukJR

    k mol K

    =

    2) to find the minimum volume, using the mass of the gas from step 1, set 1desiredp p= and ( )1BWR BWRp p V= then optimize the cost function e over the volume 1V . Note that

    11V lv Mm k mol

    =

    3) to find the maximum volume, using the mass of the gas from step 1, set 2desiredp p= and

    ( )2BWR BWRp p V= then optimize the cost function e over the volume 2V . An example of this process is provided in the next section using a spreadsheet (Microsoft Excel).

    Figure 3 Microsoft Excel Solver Dialog Screen 5.0 SPREADSHEET EXAMPLE Figure 3 shows the dialog window of the solver used to perform the optimization process. The solver can be started from the Tools menu from within Microsoft Excel. The solver is an Add-In, so be sure it has been loaded before trying to use it. For the optimization method we quote directly from the Excel help text:

    Microsoft Excel Solver uses the Generalized Reduced Gradient (GRG2) nonlinear optimization code developed by Leon Lasdon, University of Texas at Austin, and Allan Waren, Cleveland State University. Linear and integer problems use the simplex method with bounds on the variables, and the branch-and-bound method, implemented by John Watson and Dan Fylstra, Frontline Systems, Inc. For more information on the internal solution process used by Solver, contact: Frontline Systems, Inc., P.O. Box 4288, Incline Village, NV 89450-4288, (702) 831-0300, Web site: http://www.frontsys.com

    As shown in Figure 3, the Target Cell is the cost or error function (names have been defined for cell ranges such as _e1, _mass, _volume, etc.). The Changing Cells are the variables to change that affect the Target Cell. The solver will be used on the spreadsheet discussed next. Figures 4-7 show an example spreadsheet setup to do the calculations discussed in Section 3. The first column contains the variable names. The second column contains the variable values. The third column contains the variable units. The fourth column (near bottom) contains the cost functions. Each cost function is used to get m from the 0V , 0p and T , to get 1V from 1p ,T , and m , and to get 2V from 2p , T , and m , respectively. Notice the outlined boxes---values for V , m , and T are entered here. The orange boxes are the pressure calculated in different units from the BWR equation based on the values for volume, mass, and temperature above.

  • 4

    Figure 4 Spreadsheet Example a The green boxes denote values that are found through the optimization process. All optimization processes are done using the outlined boxes and the cost (error) functions. The steps below outline the procedure to follow. Steps 1-3 refer to Figure 4. Step 1 Set the initial temperature and volume to their pre-charge values. Copy the value of the volume into the volume box for the pre-charge volume (lower bottom). This is used for later calculations. Set the initial pressures. Step 2 Run the solver to minimize the pre-charge pressure error by changing the mass. The error should go to zero. Step 3 The pre-charge mass of the gas at the pre-charge pressure is now known. (11.84). Steps 4-5 refer to Figure 5.

    Figure 5 Spreadsheet Example b Step 4 Leaving the mass value as it is, run the solver to minimize the minimum pressure error by changing the volume. The error should go to zero. Step 5 The minimum accumulator volume of the gas at the minimum pressure is now known. (72.51). Copy the value of the volume down to the minimum volume green box (lower bottom). Steps 6-7 refer to Figure 6. Step 6 Leaving the mass value as it is, run the solver to minimize the maximum pressure error by changing the volume. The error should go to zero. Step 7 The maximum accumulator volume of the gas at the maximum pressure is now known. (35.93). Copy the value of the volume down to the maximum volume green box (lower bottom).

    1---Set initial V and T

    2---Optimize e over m

    3---Mass at p,V, and T

    1---Set initial ps

    4---Optimize e over V1

    5---V1 at p1 and T

  • 5

    Figure 6 Spreadsheet Example c Figure 7 highlights the minimum and maximum molar specific volumes and change in volume, along with the values for the associated accumulator reservoir. Here the maximum reservoir volume is three times the accumulator pre-charge volume.

    Figure 7 Spreadsheet Example d The reservoir volume is described in terms of the accumulator volume by

    minr rV V V= +

    The state of charge (SOC) is defined in terms of the volumes as

    max

    max min

    inV VSOCV V

    =

    .

    Note that the SOC is affected by inV which has opposite meaning for the accumulator and reservoir. 6.0 SUMMARY/CONCLUSION A method has been presented to size accumulator volumes in hybrid hydraulic applications with the accuracy of the BWR equation of state. Using a commonly available PC-based spreadsheet tool (Microsoft Excel), an optimization on a cost function (function of pressure) was employed. An accurate and complete solution was found even though the equation of state exhibited non-linear behavior. This method is simple, fast, cost effective, and adaptable to equations of state with higher complexity. While the actual energy stored is not calculated hereother tools are available using numerical integration techniques to calculate the stored energy

    ( )storedE p V dV= . CONTACT The author is an engineer at the U.S. Army Tank-automotive and Armaments Command, Research, Development and Engineering Center (TACOM-TARDEC). Interested parties can contact the author at the U.S. Army Tank-automotive and Armaments Command, ATTN: AMSTA-TR-N/MS157, Warren, Michigan 48397-5000, [email protected]. REFERENCES [1] Parker Hannifin (www.parker.com), Hydraulic Accumulator Division, Brochure 1660-USA, pg. 53. [2] Bosch Rexroth Corporation (www.boschrexroth.com) [3] Otis, D.R., Pourmovahed, A., An Algorithm for computing Nonflow Gas Processes in Gas Springs and Hydropneumatic Accumulators, Journal of Dynamic Systems, Measurement, and Control, March 1985, Vol. 107, pp. 93-94. [4] Cengel, Y.A., Boles, M.A., Thermodynamics: An

    Engineering Approach, 3rd Edition. McGraw-Hill, 1998, ISBN 0-07-115927-9, p. 85.

    DEFINITIONS, ACRONYMS, ABBREVIATIONS BWR Benedict-Webb-Rubin

    Molar specific volume and

    reservoir volumes.

    6---Optimize e over V2

    7---V2 at p2 and T

  • 6

    TACOM - U.S. Army Tank-automotive and Armaments Command TARDEC - TACOM Research, Development and Engineering Center NAC - National Automotive Center APPENDIX A BOSCH REXROTH APPLICATION NOTE See attachment.

  • 2 Accumulators Bosch Rexroth Corporation

    1. ApplicationsAccumulators are devices used to store fluid power to do the following:

    1. Store power for intermittent duty cycles thuseconomizing pump drive power

    2. Provide emergency or standby power3. Compensate for leakage loss4. Suspension in vehicles5. Dampen pulsations and shocks of a periodic nature

    2. Principals of OperationMost hydraulic systems require variable and intermittent flowrates. Energy can be saved by using the accumulator as astorage device to accept pump output flow when systemdemand is low and supplement output when demand is high.Most accumulator designs are based on the principle that gasis compressible and oil is nearly incompressible. Assume aninert gas, such as nitrogen, is contained under pressure in avessel. If hydraulic fluid is pumped into that vessel at a higherpressure than that of the original gas, the nitrogen compressesas its pressure rises to that of the fluid being pumped. Thisincrease in gas pressure is proportional to the decrease involume.The vessel now contains energy in that the volume of hydraulicfluid, stored against the pressure of compressed nitrogen gas,if released, will quickly be forced out of the vessel under thepressure of the expanding gas.Hydro-pneumatic accumulators with the gas separated from theliquid by a piston, diaphragm or bladder are by far the mostcommon type.To prevent auto ignition at high pressures, an inert gas such asdry nitrogen or helium should always be used.

    Diaphragm and bladder type accumulators differ in thestructural design of the elastic separator and the pressurevessel.

    3. Sizing and CalculationsThe majority of applications use accumulators to store energyfor intermittent duty cycles or to provide a source of emergencypower. In either case, the problem is determining the optimumsize and precharge of the accumulator.Accumulator sizing is based on the gas charge. The change ingas volume and pressure determines the amount of liquid thatcan be added or withdrawn. However, unlike mechanicalsprings, compressing a gas tends to heat it, raising thepressure above what would be expected from compressionalone. Expanding a gas tends to cool it, reducing the pressurebelow that caused by expansion alone. Either of these effectscan substantially affect accumulator sizing. Expansion (orcompression) of a gas resulting in a change of gas temperatureproduces adiabatic expansion. When an accumulator isdischarged rapidly, there is not enough time for sufficient heat transfer through the accumulator walls and adiabaticexpansion occurs.If the expansion (or compression) occurs slowly, there issufficient time for heat to be added (or subtracted) by theaccumulator wall to maintain a constant gas temperature andisothermal expansion occurs. The median of these two states ofexpansion can be partially adiabatic.

    When carrying out the calculations for an accumulator, thefollowing pressures are of primary importance:

    p0 = Gas pre-charge pressure at room temperatureand with liquid chamber drained

    p1 = Minimum operating pressurep2 = Maximum operating pressure

    The following relationships apply: the gas pre-charge pressure is to be slightly lower than the minimum hydraulicpressure so that the bladder does not continually contact the oil valve (wear).

    (1)

    The maximum hydraulic pressure is not to exceed 4 times thepre-charge pressure; otherwise, the elasticity of the bladder ordiaphragm will be adversely affected. Also, excessive changesin pressure result in considerable heating of the gas. Reducingthe pressure differential between p1 and p2 increases bladderservice life. On the other hand, it must be taken into accountthat a lower pressure differential also reduces the utilization ofavailable storage capacity.

    Bladder-type accumulators

    (2.1)

    Diaphragm-type accumulators

    (2.2)

    p0 0.9 p1

    p2 4 p0

    p2 4 p0

  • Bosch Rexroth Corporation Accumulators 3

    Oil volumesThe gas volumes V0 V2 correspond to the pressures p0 p2.Here, V0 is the rated volume of the accumulator.

    The available oil volume V corresponds to the differencebetween the oil volume V1 and V2.

    (3)

    The variable gas volume for a given pressure difference isdetermined according to the following equations:a) For isothermal change of state of gases, the following

    equation applies:

    (4.1)

    The isothermal equation is used when the change in the gasvolume takes place so slowly that there is sufficient time for thecomplete exchange of heat to take place between the nitrogenand its surroundings. The result is a constant temperature.b)For adiabatic change of state of gases, the following

    formula applies:

    (4.2)

    n = relationship of the specific heats of the gas (adiabaticcomponent); n = 1.4 for nitrogen. The equation for adiabaticchange of state is used when the change in the gas volumetakes place so rapidly that the temperature of the nitrogen alsochanges.In most cases the changes of state tend to follow the adiabaticrather than the isothermal laws. It is often the case that thecharge takes place isothermally and the discharge adiabatically.Considering the equations (1) and (2), V is about 50 to 70%of the rated accumulator volume. The following formula can actas a guideline for sizing accumulators:

    (5)

    Calculation diagramsThe formulae (4.1) and (4.2) are converted into diagrams onpages 4 to 6 for graphic calculation purposes. Depending onthe type of problem, the available oil volume, the accumulatorsize or the pressures can be determined.

    Correction factors K i and KaThe formulae (4.1) and (4.2) apply to ideal gases only. Inpractice, at pressures above 200 bar (2900 psi), the behaviorof real gases deviates markedly from that of the ideal gases.This makes it necessary to use correction factors. These are tobe taken from the following diagrams. The correction factors,with which the ideal discharge volume V must be multiplied,are in the range of 0.6 1.

    V= V2 V1

    p0 V0 = p1 V1 = p2 V2

    p0 V0n = p1 V1n = p2 V2n

    V0 = 1.5 3x V

    1.0

    0.9

    0.8

    0.7

    0.60.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

    P1/P2

    Ki

    P2 = 200 bar

    P2 = 300 bar

    P2 = 400 bar

    1.0

    0.9

    0.8

    0.7

    0.60.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

    P1/P2

    Ka

    IsothermalAdiabatic

    real = ideal KA real = ideal Ki

    P2 = 200 bar

    P2 = 300 barP2 = 400 bar

  • 4 Accumulators Bosch Rexroth Corporation

    Using the DiagramsWith the pre-charge pressure (p0) and the minimum andmaximum system pressures (p1 and p2) known, the availablevolume can be determined from the charts. Vertical lines aredrawn from p1 and p2 to intersect the appropriate pre-chargecurve. From the points of intersection, horizontal lines are thendrawn to the left axis. Here V1 and V2 can be determined for thevarious sizes of accumulators. The difference between thesevalues is the available volume.Similarly, pressures can be determined if the volume is known.

    p 0

    S2

    S1

    P1 P2

    V2

    V1

    V (cu. in.)

    p (psi)

    Gas pre-charge pressure

    Availableoil volume

    Working pressure range

    n

    p

    How to use the calculation diagrams

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  • Bosch Rexroth Corporation Accumulators 5

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  • 6 Accumulators Bosch Rexroth Corporation

    Installation and Operating InstructionsMounting and Installation

    BLADDER TYPE ACCUMULATORS MUST BE MOUNTED IN A VERTICALPOSITION WITH THE OIL VALVE AT THE BOTTOM. PLEASE CONSULT THEFACTORY IF OTHER MOUNTING POSITIONS ARE NECESSARY.

    Mounting of Diaphragm Accumulators is unrestricted. Allaccumulators must be rigidly installed using clamps andsupport brackets specifically designed for accumulatormounting. Oil valve ports must not be used to support theweight of the accumulator.

    CAUTION - DO NOT use gas or oil valves as lifting points. Theaccumulator shell is a pressure vessel and must not be altered.DO NOT weld or machine pressure vessels.

    Improper installation may result in damage to the oil or gasvalve, accumulator shell, or seals. Exercise care not to paintover rating nameplate or the warning label.

    GeneralHydraulic circuits incorporating accumulators may storehydraulic oil under pressure depending on the function of theaccumulator in the system. Therefore, the system may remainpressurized after the pump is turned off.CAUTION - Prior to performing any maintenance or systemmodifications, bleed off any stored system pressure.Completely release all hydraulic fluid pressure in a safecontrolled manner using appropriate valving. Installation ofan automatic accumulator discharge valve in the hydrauliccircuit is recommended.Accumulator repairs must be performed by trainedhydraulic service personnel experienced in servicingaccumulators. Contact your local authorized distributor forapplication or repair assistance.

    Bladder accumulatorsBladder type are generally delivered with a nitrogen pre-chargepressure of approximately 50 psi (3 bar) . After installation andprior to initial start-up, the pre-charge pressure (p1) must be setto the application requirements, or machine manufacturersspecifications.

    Diaphragm accumulatorsDiaphragm type are generally delivered without pre-chargepressure. The pre-charge pressure must be set to the applica-tion requirements or machine manufacturers specificationsprior to initial start-up.CAUTION - Improper accumulator pre-charge may result indecreased life or failure of the bladder or diaphragm.

    10.0 10.0

    5.0 2.0

    2.0

    15.035.0

    60.0

    70.0130.0

    120.0

    110.0

    100.0

    90.0

    70.0

    50.0

    30.0

    20.0

    80.0

    60.0

    40.0

    20.0

    30.0

    40.0

    50.0

    10.0

    15.0

    20.0

    25.0

    30.013.0

    11.0

    8.0

    5.0

    1.0

    14.0

    12.0

    9.0

    6.0

    3.0

    10.0

    7.0

    4.0

    7.0

    6.0

    4.0

    1.0

    5.0

    3.0

    170 85 43 21 10 20 6040 80 100

    140

    200

    300

    400

    600

    1000

    1400

    2000

    3000

    4000

    5000

    6000

    NOMINAL ACCUMULATORSIZE Vo IN CUBIC INCHES

    OPERATING PRESSURES P1 and P2 (PSIG)

    AVA

    ILA

    BLE

    VO

    LUM

    E (

    CU

    BIC

    INC

    HE

    S)

    PRESSURE-VOLUME CURVE, ISOTHERMAL RELATIONSHIP, Diaphragm Type Accumulator

    P 0G

    AS

    PREC

    HA

    RG

    EPR

    ESSU

    RE(P

    40 60 80

    100

    140

    300

    400

    600

    1000

    1400

    200020020

  • Bosch Rexroth Corporation Accumulators 7

    1. Accumulator 3. Check valve2. Bleed or automatic 4. Pump

    discharge valve 5. Oil pressure gauge

    12345

    6

    7

    8

    9

    10

    Tightening torque for valve guard175350 lb-in (2040 Nm)

    *

    Checking the gas pre-charge pressureBleed off hydraulic system pressure. After the accumulator hasbeen put in service, the pre-charge pressure (p0) should bechecked with an accumulator charging and testing device atleast once in the first week. If this check reveals no loss inpressure, the pre-charge should be checked on the followingschedule:

    1st Check 1 week2nd Check 3 months3rd Check 1 year4th & Continued yearly

    If the gas pre-charge is low, investigate cause and correct.Possible causes of lost pre-charge pressure include leaking ordamaged gas valve, or damaged bladder.Testing pre-charge pressure p0 Completely release accumulator hydraulic system pressure in asafe controlled manner. Install the charging and testing deviceonto the gas valve (see Fig. 1, Item #4). While depressing thebutton on the charging device, the gauge will indicate the gaspressure.

    FIG.1

    2

    1

    3

    4

    5

    To System

    FIG.2 Typical Circuit

    Charging the accumulatorCAUTION - USE only NITROGEN for charging accumulators.NEVER USE OXYGEN OR AIR, due to the risk of explosion.Close the drain valve on the charging and testing device andconnect the hose to the nitrogen bottle.Remove the valve guard and cap and screw the charging andtesting device onto the gas valve. More detail information isprovided in the instruction sheet furnished with the chargingand testing device. Open the gas shut-off valve on the nitrogenbottle and allow the gas to flow slowly into the accumulator.Close the shut-off valve frequently and check the value on thepre-charge by depressing the button on the charging device.If the pre-charge pressure is too high, it may be reduced byopening the drain valve and carefully depressing the button onthe charging device.NOTE: The pre-charge pressure will vary depending on the gastemperature. Once the desired pre-charge is reached, it isnecessary to wait 2 minutes until the gas temperature hasequalized. Once again the pre-charge pressure needs to bechecked and adjusted if necessary.Unscrew the charging and testing device and replace the valveguard and cap (see Fig. 1, Items #1 & 2) and torque to specifi-cations. A check for leaks with a soapy solution should follow. If a leak is found, it should be repaired following recommendedrepair procedures. If the gas valve core is replaced, use onlyvalve cores approved for accumulator service, NEVER USE ANAUTOMOTIVE TYPE VALVE CORE.

    1. Valve guard* 6. Poppet valve2. Valve cap 7. Gauge port3. Gas valve core 8. Hydraulic line4. Gas valve body 9. Clamp5. Name plate 10. Support bracket

    Nitrogen

    Nitrogen

    a0.025102(l/g-mol)^3atmBarF109.53141.93177.93213.93249.93285.93321.93357.93

    A01.053642(l/g-mol)^2atmC28.8546.8566.8586.85106.85126.85146.85166.85

    b0.002328(l/g-mol)^2litersvmol/K302320340360380400420440

    B00.040743(l/g-mol)100.0236649121462.2221909.5222403.4122894.7023383.9423871.5124357.7424842.85

    c728.410(l/g-mol)^3(K)^2atm200.047329821086.531179.151281.761384.101486.241588.211690.051791.78

    C08059.000(l/g-mol)^2(K)^2atm400.09465964301.62328.37358.06387.73417.37447.00476.62506.22

    alpha0.000127(l/g-mol)^3600.14198946184.75199.66216.19232.69249.18265.64282.09298.53

    gamma0.005300(l/g-mol)^2800.18931928134.97145.20156.55167.87179.17190.47201.75213.02

    R0.082054(l/g-mol)atm/(K)1000.2366491106.81114.58123.19131.78140.36148.93157.49166.04

    volume35.93liters1200.283978920188.5594.80101.73108.64115.55122.45129.34136.22

    mass11.84kg1400.331308740175.7080.9286.7192.5098.27104.04109.81115.57

    spec. vol0.003035m^3/kg1600.378638560166.1470.6275.6080.5785.5390.4995.44100.39

    vmol0.085023m^3/kmol1800.425968380158.7462.6767.0371.3975.7480.0884.4288.76

    T302.00K2000.473298200152.8456.3460.2264.1067.9771.8375.7079.56

    28.85C2200.520628020148.0351.1854.6758.1661.6565.1368.6272.10

    109.53F2400.567957840144.0246.8950.0653.2456.4159.5862.7565.92

    P345.42atm2600.615287660140.6343.2646.1849.0952.0054.9157.8160.72

    35000.00kPa2800.662617480137.7340.1642.8545.5448.2350.9153.6056.28

    350.00bar3000.709947300135.2237.4739.9742.4744.9747.4649.9652.45

    5076.29psi3200.757277120133.0235.1237.4639.7942.1244.4546.7849.11

    =8.134kJ/(kmol K) / 101.325 kPa3400.804606940131.0833.0535.2437.4339.6241.8043.9846.17

    volumeP(bar)errormass3600.851936760229.3631.2133.2735.3337.3939.4541.5043.56

    PreCharge80.0013546225.0011.843800.899266580227.8129.5731.5133.4635.4037.3539.2941.23

    Min72.5115040000.000.00612588824000.946596400226.4328.0929.9331.7833.6235.4637.3039.14

    Max35.933500.000.00303511084200.993926220225.1726.7528.5030.2532.0033.7535.5037.25

    dV36.594401.041256040224.0325.5327.2028.8730.5432.2033.8735.53

    Rmax.240.004601.088585860222.9924.4226.0127.6129.2030.7932.3833.97

    Rmin.203.414801.135915680222.0323.4024.9326.4527.9729.5031.0232.54

    5001.183245500221.1522.4723.9325.3926.8528.3129.7731.22

    get Vgmin,Vgmax,Vrmin,Vrmax,initial spec.vol, and T

    -393.18kJ